It is worth emphasizing again the necessity for the “qubit threads” to satisfy the constraints on fluxes \({F_{ij}}\)  given by equation (REF ). This is because essentially \({F_{ij}}\)  can be understood as a generalization of the multipart case of mutual information \(I\) . In particular, in the case involving only three elementary regions, we have (REF ). Furthermore, according to this scheme, one can obtain the expression of PEE in terms of flow fluxes [1]}:
\({s_R}\left( {{A_s}} \right) = \sum \limits _t {{F_{st}}} ,\,\,\,\, s \in \left\lbrace  {a,a + 1, \cdots ,b} \right\rbrace , t \notin \left\lbrace  {a,a + 1, \cdots ,b} \right\rbrace .\) 
